Let x and y be any two vectors in R^ 3 . a. Prove that the vectors ||y||x + ||x||y and ||y||x - ||x||y are orthogonal. b. Show that ||y||x + ||x||y bisects the angle between x and y.

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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A: According to the given information, it is required to prove the inequality.

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A: By Cauchy-Schwarz Inequality for the vectors, we have

Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

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A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

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A: I have append the formula in solution part

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A: Solution :-

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Q: . Let x and y be two orthogonal vectors. Then prove that

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A: Let X=x,y,z,t be the vector that is orthogonal to u= (2, 1, - 4, 0), v= (-1, - 1, 2, 2) and w= (3,…

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A: